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2024 | Book

Fundamentals of Aeroelasticity

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About this book

This textbook provides the fundamentals of aeroelasticity, with particular attention to problems of interest to aeronautical engineering. The mathematical methods and tools applicable to the modern modeling of general aeroelastic problems are presented, discussed, and applied to fixed-wing aircraft configurations. It is composed of ten chapters divided into two parts: (I) aeroelastic modeling and analysis and (ii) mathematical tools. The six chapters that compose the first part start from the historical background of the discipline, then present the methods for coupling structural dynamics and unsteady aerodynamics for the aeroelastic modeling of the typical wing section, and then extend them to applications for twisted, tapered, swept finite-wing configurations. In this context, particular attention is paid to the presentation, interpretation, and discussion of the available unsteady sectional aerodynamic theories, both in the time and frequency domain, providing a broad scenario of the formulations that can be used for conventional and non-conventional aerodynamic/aeroelastic applications. For a modern view of aeroelasticity, a significant portion of the textbook deals with illustration and discussion of three-dimensional aerodynamic theories and computational methods for the determination of unsteady aerodynamic loads over lifting bodies in incompressible and compressible flows, as well as to the introduction and explanation of methodologies for the identification of reduced-order, state-space aerodynamic/aeroelastic operators suitable for stability (flutter) analysis and control purposes. A chapter is dedicated to the theories and approaches for aeroservoelastic modeling. In the second part of the textbook, additional chapters provide theoretical insights on topics that enrich the multidisciplinary knowledge related to widely applied methods and models for the analysis and solution of aeroelastic problems. The book serves as a reference tool for master's degree students in aeronautical/aerospace engineering, as well as researchers in the field of aeroelasticity.

Table of Contents

Frontmatter

Aeroelastic Modelling and Solution Methods

Frontmatter
1. Introduction to Aeroelasticity
Abstract
This chapter describes the discipline of Aeroelasticity by presenting the historical framework within which it has developed over the last century and the physics of the phenomena involved. It makes reference to the earliest aeroelastic events that occurred in aeronautical applications and thus motivated the work of the pioneers of aeroelastic studies, and it provides a classification of all the aeroelastic phenomena that must be taken into account during aircraft design. The organisation and contents of the book are explained at the end of the chapter.
Massimo Gennaretti
2. The Wing Typical Section
Abstract
This chapter introduces the wing typical section, which is the basic two-dimensional model for the study of phenomena of aeronautical interest. It is considered in the context of the development and solution of aeroelastic models of varying accuracy and complexity, aimed at stability and response analyses. Steady, quasi-steady and unsteady formulations for airfoil aerodynamics are outlined and applied, with the theories of Theodorsen, Wagner and Küssner-Schwartz included among them. Methodologies for aeroelastic modelling in state-space form are illustrated, and the problem of gust response is examined.
Massimo Gennaretti
3. Finite Wings
Abstract
The aeroelastic modelling presented in Chap. 2 is extended here to include finite, fixed wings. The equivalent beam model is introduced for the purpose of describing the structural dynamics of unswept and swept wings and is coupled with unsteady aerodynamic formulations. The three-dimensional wake vorticity effects are discussed and included in the unsteady lifting line aerodynamic model. The application of the Galërkin’s method for the solution of aeroelastic problems is explained and the state-space form of the resulting aeroelastic operator is obtained by the rational approximation of the transfer functions collected in the aerodynamic matrix.
Massimo Gennaretti
4. The Panel Method for Wing Aeroelasticity
Abstract
This chapter presents the panel method used for the solution of incompressible potential flows around lifting bodies and examines its application in aeroelastic modelling. After a reminder of the fundamental aspects of potential flow theory, the boundary integral formulation approach for the solution of non-circulatory potential flows and the boundary element method (BEM) for numerical application are presented. Subsequently, the concept of potential wake is introduced and the boundary integral formulation and corresponding BEM solution are extended to deal with lifting wings in order to determine the aerodynamic matrix and the aeroelastic operator accordingly, based on a fully three-dimensional aerodynamic solution.
Massimo Gennaretti
5. Elements of Aeroservoelasticity
Abstract
The basic concepts relating to the application of automatic control systems to improve aeroelastic stability and response characteristics of wing configurations are presented in this chapter. The development of an aeroservoelastic system is illustrated in a two-dimensional configuration consisting of the typical section model that has been extended by the introduction of a movable trailing edge flap (the aileron). The equations that govern the aeroelasticity of the typical section-aileron system are derived and their application is discussed in the context of an optimal control methodology for the synthesis of feedback control laws for stabilisation. The introduction of a state observer is also examined.
Massimo Gennaretti
6. Finite Wings in Compressible Flows
Abstract
This chapter extends the aerodynamic panel method solution for aeroelastic applications, presented in Chap. 4, to compressible flows. After the introduction of the Green’s function for the wave equation, which includes the delay effects of flow compressibility, the boundary integral formulation for lifting wings in subsonic flight is derived and the BEM approach is applied to determine the aerodynamic matrix that contributes to the definition of the aeroelastic operator in compressible flows.
Massimo Gennaretti
7. Rotary-Wings
Abstract
The basic concepts and mathematical tools for the development of the aeroelastic models of rotary wing systems are outlined. The chapter begins with a general introduction to the problems associated with the aeroelasticity of rotary wings, including a physical insight into the nature of the specific phenomena involved. Next, the development of simplified aeroelastic models for rotary wings in hovering and forward flight is presented and the characteristic mechanical and aerodynamic contributions are discussed. Finally, the solution methods that are of interest to rotorcraft designers are described.
Massimo Gennaretti

Mathematical Tools and Methods

Frontmatter
8. Elements of the Calculus of Variations
Abstract
This chapter explains the basic principles of the theory of the calculus of variations. Having defined what a functional is, the technique for identifying its minima through the calculus of variations is presented for the classes of problems of interest for the development of the aeroelastic models presented in Part I of the textbook. A specific application of the calculus of variations aimed at defining the equation that governs the dynamics of a bending beam as a result of Hamilton's variational principle is discussed in detail to show the potential of this approach.
Massimo Gennaretti
9. Elements of Differential Geometry
Abstract
This chapter introduces fundamental elements of the differential geometry that deal with vector algebra and calculus in curvilinear coordinates. The covariant and contravariant basis vectors, surface and volume mapping and the gradient operator in curvilinear coordinates are presented and discussed. In this textbook, the curvilinear coordinates are suitably introduced in order to define the transfer functions collected in the aerodynamic matrix resulting from the BEM solutions presented in Chaps. 4 and 6.
Massimo Gennaretti
10. Notes on Galërkin’s Method
Abstract
The Galërkin method is used to obtain an approximate weak form of the solution of differential equations. This chapter describes the procedure for implementing this methodology, defines the conditions for its applicability and discusses relations with alternative approaches such as the Rayleigh–Ritz method. In this textbook, the method is applied to solve the equations that govern the aeroelastic behaviour of a wing.
Massimo Gennaretti
Backmatter
Metadata
Title
Fundamentals of Aeroelasticity
Author
Massimo Gennaretti
Copyright Year
2024
Electronic ISBN
978-3-031-53379-2
Print ISBN
978-3-031-53378-5
DOI
https://doi.org/10.1007/978-3-031-53379-2

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